Les programmes présentés ici sont tous en ** matlab **. Ils requierent (presque) tous l'instalation préalable de la statistic toolobox. Cette section sera étoffée au fûr et a mesure.

# Progams related to "Estimation of surface area"

include tools for "generalization of the maximal-spacings in several dimension and a convexity test"

- Surface estimator based on Crofton with Devroye Wise based method croftonDW.m

Input : X the sample, r the radius for the Devroye wise estimator, Ntheta the number of MC angle sample, Ny the number of MC "lengh" sample (the total MC Croton drawn is Ntheta * Ny) and N0 (a maximum number of intersections)

Output : measurf the estimated surface area, and meassurfN0 the estimated surface area given an Oracle information on N0. - Surface estimator based on Crofton with r-convex hull estimator croftonCr.m

Input : X the sample, Ntheta the number of MC angle sample, Ny the number of MC "lengh" sample (the total MC Croton drawn is Ntheta * Ny) and kdens a number of neighbor for density estimation

Output : measurf the estimated surface area.

The choice of r for the r convex hull is automatic with respect to this work .

To run Crofton Cr requires to download also:- alphashapemaxspace2.m

Input : X the data and k a number of neighbors for density estimation.

Output : sorted list of simplices trit, with associated radius Rt (increasing) and pvalue for test pvalMS so, that with a level alpha the automatic radius can be found with :

ii=find(pvalMS>=0.05); r=Rt(max(ii));

**Remark : if r is not max(Rt) then one can decide that the support is not convex. according to "generalization of the maximal-spacings in several dimension and a convexity test"** - alphahull.m

Input : X the data and r_0 a raduis.

Output : Oout a list of Nout points and Rout a list of Nout raduis; Pout a list of Nout' points and normout a list of Nout' unit vector

so that the r_0 convex hull of X is the union of B(Oout, Rout) with the union of HSout (half spaces X-Pout.normout less than 0). - rayonscir.m

Input : tri a simplicial complex and X the data sample

Output : R the raduis of each simplex and centre its center.

also works with d leq D dimensional simplex when X is D dimensional - unifsuprnd3.m

Input : tri a simplex, X the data (verices) and Nsim the size of the output sample

Output : Y the result of an uniform drawn on the complex tri,

- volumesimplexe2.m

Input : X the vertex of a simplex (for instance X(tri(i,:),:)) the simplex may be d dimensional (d+1) points in R^D with d less than D

Output : the d dimensional volume of the simplex, Ind the simplex in which any point of Y belong and W its barycenter coordinates

- alphashapemaxspace2.m